Abstract : We report the results of ALMA observations of a protoplanetary disk surrounding the Herbig Ae star AB Aurigae. We obtained high-resolution (0.1"; 14 au) images in $^{12}$CO (J=2-1) emission and in dust continuum at the wavelength of 1.3 mm. The continuum emission is detected at the center and at the ring with a radius of $\sim$ 120 au. The CO emission is dominated by two prominent spirals within the dust ring. These spirals are trailing and appear to be about 4 times brighter than their surrounding medium. Their kinematics is consistent with Keplerian rotation at an inclination of 23 degree. The apparent two-arm-spiral pattern is best explained by tidal disturbances created by an unseen companion located at 60--80 au, with dust confined in the pressure bumps created outside this companion orbit. An additional companion at r of 30 au, coinciding with the peak CO brightness and a large pitch angle of the spiral, would help to explain the overall emptiness of the cavity. Alternative mechanisms to excite the spirals are discussed. The origin of the large pitch angle detected here remain puzzling.